A transmission device of this kind is described in JP2002235832A as a component part of an electric drive unit. The electric drive unit has a rotor shaft, which is the input shaft of a transmission device. The transmission device is formed from a differential gear unit and a reduction stage. The reduction stage is a planetary drive, the sun gear of which is seated on the rotor shaft. The differential is a “spur gear differential”, in which the differential gears are planet gears and the output gears are sun gears. Each sun gear is seated on an output shaft of the differential. The torques input via the input shaft/rotor shaft are introduced into the differential via the reduction stage and are distributed by the differential to the output shafts and hence to driven vehicle wheels. The rotor shaft is a hollow shaft, through which one of the output shafts is passed. In this arrangement, an annular gap is formed between the rotor shaft and the output shaft. The output shaft and the respective sun gear are connected to one another for conjoint rotation by splines. Apart from wet-rotor electric motors, the region of the electric machine between the stator and the rotor should be kept free of lubricating oil. However, the transmission device is lubricated with transmission oil. There are drive units in which the annular gap between the output shaft and the rotor shaft is used as an oil duct in order, for example, to feed lubricating oil to a rolling bearing situated axially on the outside. However, there are also drive units in which the rolling bearing situated on the outside is lubricated via other paths or has lifetime lubrication.